Multipath signals in a wireless environment can result in interference and degraded communication performance. In principle, based on received wireless signals as a function of time and space (in communications systems with spatial diversity), wireless-communication parameters such as the time of arrival can be estimated. For example, a superposition of wireless signals having different delays in the time domain results in a summation of exponentials in the frequency domain. Consequently, for well-separated frequencies, Fourier techniques can be used to estimate the minimum time of arrival, and thus to identify the wireless signals associated with line-of-sight communication.
In many applications, the frequency or tone separations are close to the Fourier resolution. This often requires the use of so-called ‘high-resolution techniques’ to identify the wireless signals associated with line-of-sight communication. For example, a covariance matrix based on the wireless signals can be used to deconvolve the wireless signals in a multipath wireless environment, and thus to identify the wireless signals associated with line-of-sight communication.
However, it can be difficult to determine the covariance matrix. Notably, there is often insufficient data available to uniquely determine the covariance matrix. For example, in order to determine the covariance matrix uniquely, multiple instances or repetitions of the wireless signals may need to be acquired. In time-sensitive applications, such repeated measurements are unavailable. Consequently, the determination of the covariance matrix may be underdetermined, which can complicate and confound attempts at identifying the wireless signals associated with line-of-sight communication. In turn, the resulting errors may degrade the communication performance, which is frustrating for users.
In principle, sub-band or super-resolution techniques can be used to estimate the minimum time-of-arrival of wireless signals. However, in practice it may be difficult to use many sub-band or super-resolutions techniques when there are a large number of multipath signals. Notably, the large number of multipath signals may constrain matrix operations that are used in sub-band or super-resolutions techniques, such as eigenvalue decomposition. For example, the computation requirements for eigenvalue decomposition may scale as the cube of the number of dimensions, such as the number of time, frequency and/or spatial samples. Consequently, it may be computationally impractical to use many sub-band or super-resolution techniques to determine the minimum time-of-arrival of wireless signals.